In order to work with seqeunces, we must first have an understanding of what they are and how to construct them.
A sequence is a function S whose domain is the set of natural numbers, \mathbb{N}.
Informally a sequence is simply a collection of numbers, such that the order matters. If you swap the positions of two values in a sequence, the result will not be equivalant to the original sequence.
A sequence S is notated (s_n) or as a list of elements
(s_1,s_2,s_3,\ldots)
The function S \colon \mathbb{N} \to \mathbb{Q} such that n \rightarrowtail \frac{1}{n} is a sequence. We use the notation (1/n) as an abbreviation for
\left(1,\frac{1}{2},\frac{1}{3},\ldots\right)
Similarly, the sequence S \colon \mathbb{N} \to \mathbb{N} where n \rightarrowtail 2n is denoted (2n), abbreviating
(2,4,6,\ldots)
Normally we will consider sequences where the codomain is \mathbb{R}.